UPDATE: It seems you need to be in Japan when you enter the Arena. Once I tried it this way the Rock Hyraxes started dropping (at a very slow rate but it beats zero).
It's bad enough that Zynga slapped a 30 day timer on the Japan City Mission. If you recall, Los Angeles doesn't have a timer. Now many will be forced to try to master districts they aren't ready for and those who did will have to endure the ruby level jobs. I won't even get into the requirements for the Syndicate jobs. What's even more annoying in this game is when you do things the way you are supposed to and the expected outcome never happens. In almost all Missions we have had in the past few years there is always a task to loot something by doing damage in the Arena. 90% of the time the items never show up. After doing 46 Shootout Arenas and dealing 1,052,656 damage I have zero Rock Hyraxes and I'm not even surprised. If Zynga can't fix this reoccurring bug than they could be smart and remove this type of task. After a day or two of white screens, most of us are already behind in this Mission and this isn't helping anyone.